Reports should be organized according to the following structure and
should include all of the subheadings except for the title page.

Title Page A descriptive title must clearly identify the topic,
the nature of the research, for example, An Analysis of the Mineral
Composition of the Water in Greasy Lake. The writer's name and other
relevant information such as the course, the teacher, and the date the
report is due follow. These items are centered line by line and the
page has even margins top and bottom.

Abstract A separate page for the abstract presents a short summary
of the significant points of the paper, usually 250 or fewer words.

Introduction In a paragraph or two, the introduction states
the problem and the purpose of the report, including a clear statement
of the hypothesis. This section identifies the outcome as well as necessary
background information readers need to understand the context. It includes
definitions of terms that readers need to know. If the teacher or editor
requires a review of existing literature on the topic, that information
belongs in the introduction. Here, as elsewhere in the paper, documentation
of sources does not use footnotes but does use parenthetical in-text
citations with the name-year method, for example (Wiggins, 1984). Paragraph
rather than list structure is used for this section of the paper.

Materials and Methods Precise, detailed information about the
experiment or study includes exactly what was done, using exact measurements
rather than approximate measurements. Diagrams and tables may accompany
this section but cannot substitute for clear explanations. Methods used
to verify the authenticity of data should be included.

Materials should be incorporated within the narrative rather than in
a list. The narrative should be written in past tense rather than as
instructions in the imperative present (for example, I filled six petri
dishes with agar or Six petri dishes were filled with agar not Fill
six petri dishes with agar).

From the details in this section, readers should be able to duplicate
the experiment.

Results This data section contains little explanatory information
and no judgments or conclusions. Instead, it presents tables, graphs,
and diagrams with brief explanations. Each table must have a heading
and must be numbered consecutively.

Discussion This section explains what happened in the experiment
and how the researcher derived the conclusions. If the data refute the
original hypothesis, explanations are appropriate. The meanings and
significance of the findings appear here.

Literature Cited This bibliographical section begins on a separate
page from the text. An alphabetical list by author's last name includes
all publications and studies mentioned in the report, following one
of the accepted style guides for the field of research, for example,
American Psychological Association style (APA) or Council of Biology
Editors style (CBE).

Options Some writers present a separate section of conclusions; however,
conclusions often appear in the discussion section. An acknowledgments
page after the abstract is appropriate if other people assisted with
the research, the experiment, or the preparation of the report.

Sample Report

Series AC Circuits

by Student Name

ETR 114 91B W. T. Blythe

DUE: JANUARY 29, 1992

SUBMITTED: JANUARY 29, 1992

LATE POINTS ____________

FORM _____ CONTENT ______

I. PURPOSE

The purpose of this lab is to investigate the characteristics of series
AC circuits.

II. THEORY:

The behavior of series AC circuits is similar to those of DC series
circuits. The basic laws such as Ohm's Law, Kirchhoff's Current and
Voltage Laws, Current and Voltage Divider Rules, and the additive properties
of resistance and power hold true. The differences lie mainly in the
methods of analysis used for AC circuits which are somewhat more complicated
than those used for DC analysis.

The circuit consisting of a resistor, a capacitor, and an inductor
in series was placed in series with a frequency generator. Voltages
were measured, recorded and compared with calculated values. Since resistances
in series can be rearranged in any given order, it was possible to measure
each value with respect to ground, which is sometimes necessary when
using an oscilloscope.

Although the term "resistance" was used in the above discussion, the
actual term is really impedance. The impedance of the resistor at most
frequencies (below a few hundred kilohertz) is equal to its resistance
value. In a purely resistive circuit, resistance is unaffected by a
sinusoidal voltage. Therefore, the current through and the voltage across
the resistor will be in phase. The use of vectors known as phasor algebra
most easily expresses this type of relationship. This mathematical "tool"
expresses the magnitudes of currents, voltages, and impedances along
with the value of the phase angle in degrees. Using this tool, one can
create an impedance diagram by plotting resistance on the positive horizontal
(real) axis, and reactance on the vertical (imaginary) axis.

In an ideal inductor, the voltage is said to lead the source current
by 90 degrees. The inductive reactance is, therefore, plotted on the
positive imaginary axis which is denoted as "j". In an ideal capacitor,
the voltage lags the source current by 90 degrees. The phase angle,
therefore, is 90 degrees and the capacitive reactance is plotted on
the negative imaginary axis which is denoted as "- j". These values
can be expressed in two formats. In rectangular form, the value is composed
of the real value along with the imaginary value. This is known as a
complex number with the format: C = A + jB. The other form is polar
form, which expresses the resultant magnitude and the phase angle with
the format: C = C .

The effects of frequency on reactance are also to be considered. Since
inductive reactance is equal to the product of (2 )(f)(L), reactance
increases with frequency. Capacitive reactance equals 1/(2 *)(f)(c),
which means that as frequency increases, reactance decreases. Analysis
for a given circuit is, therefore, limited to a specific frequency.
Because the components are not ideal, phase relationships may vary from
the ideal 90 degrees. A voltage diagram of measured voltages should,
however, indicate a strong similarity to the calculated voltages.

PROCEDURE:

1. Measure all components on the impedance bride. (Also measure the
inductor's resistance.) 2. Using the oscilloscope and a small series
resistor, calculate the effective resistance and inductance of the inductor.
3. Construct a series circuit with the components and a frequency generator.
4. Measure voltage across each element with respect to ground. (rearranging
as necessary) 5. Design an equivalent circuit. (two element) 6. Draw
a phasor diagram with measured and predicted results on the same axes
but with different colors. 7. Repeat steps 1 through 5 at 4K.

RESULTS: (See print copy available at the Writing Center)

CONCLUSIONS:

This lab definitely proved to be a challenge both in making the measurements
and performing the calculations. Though applications of the basic laws
of DC circuits were used, the mathematics necessary for AC analysis
was more demanding. It was hard to be accurate beyond two significant
figures when making measurements with the oscilloscope. Certainly, this
lack of precision was part of the reason for inaccuracies. Another possible
cause for error is the inductor. The resistance (67.5 ohms) had to be
accounted for when calculating total impedance and when calculating
the voltage across the inductor itself. But more important may be the
effect of power losses due to hysteresis, eddy currents, skin effect,
and radiation. Since radiation losses only occur at radio frequencies,
these can be ruled out at 2khz, but the bottom line is that any loss
of power translates into a gain of effective resistance. If the total
power is divided by the square of the total current, the result is the
effective resistance. (by rearranging P = I2R) The calculated result
for the lab circuit was 395 ohms which matches the resistance of the
equivalent circuit. The measured value is 413 ohms which makes a difference
of 18 ohms in the effective resistance.